This paper describes the design, kinematic analysis, control architecture and experimental validation of a novel 3-degree-of-freedom (DOF) robotic surgical instrument for use in minimally invasive surgery. This instrument contains a wrist mechanism that can enter the body through incisions of about 18 mm and that can be actuated extra-corporally with rigid push-pull rods passing through linear bearings in the instrument shaft. The rigid transmission and parallel architecture of this mechanism also makes it back-drivable and suitable for force estimation and control. With this instrument, it is possible to achieve and even surpass the 2 DOF bending motion that the human wrist is capable of (90-degree pitch-flexion/extension and yaw-radial/ulnar deviation) and the 1 DOF translation motion in the forward/backward directions. A prototype of the proposed design has been manufactured and assembled and has been controlled with joint space PID controllers with disturbance observers. The results of position control and back-drivability experiments on the system validate our proposal.